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<h1>N4JS Language Specification</h1>
<div class="details">
<span id="author" class="author">2019-08-08 13:15:33 CEST</span><br>
<span id="revnumber">version 0.9</span>
</div>
<div id="toc" class="toc2">
<div id="toctitle">Table of Contents</div>
<ul class="sectlevel1">
<li><a href="#_introduction">1. Introduction</a>
<ul class="sectlevel2">
<li><a href="#_notation">1.1. Notation</a>
<ul class="sectlevel3">
<li><a href="#_grammar-notation">1.1.1. Grammar Notation</a></li>
<li><a href="#_type-judgments-and-rules-and-constraints-notation">1.1.2. Type Judgments and Rules and Constraints Notation</a>
<ul class="sectlevel4">
<li><a href="#_typing-rules-and-judgments">1.1.2.1. Typing Rules and Judgments</a></li>
<li><a href="#_types-of-an-element">1.1.2.2. Types of an Element</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#_auxiliary-functions">1.2. Auxiliary Functions</a>
<ul class="sectlevel3">
<li><a href="#_binding">1.2.1. Binding</a></li>
<li><a href="#_merging-types">1.2.2. Merging Types</a>
<ul class="sectlevel4">
<li><a href="#_logic-formulas">1.2.2.1. Logic Formulas</a></li>
</ul>
</li>
<li><a href="#_symbols-and-font-convention">1.2.3. Symbols and Font Convention</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="grammar.html#_grammar">2. Grammar</a>
<ul class="sectlevel2">
<li><a href="grammar.html#_lexical-conventions">2.1. Lexical Conventions</a>
<ul class="sectlevel3">
<li><a href="grammar.html#_identifier-names-and-identifiers">2.1.1. Identifier Names and Identifiers</a></li>
<li><a href="grammar.html#_this-keyword">2.1.2. This Keyword</a></li>
<li><a href="grammar.html#_regular-expression-literals">2.1.3. Regular Expression Literals</a></li>
<li><a href="grammar.html#_automatic-semicolon-insertion">2.1.4. Automatic Semicolon Insertion</a></li>
<li><a href="grammar.html#_jsdoc">2.1.5. JSDoc</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="names.html#_names">3. Names</a>
<ul class="sectlevel2">
<li><a href="names.html#_access-control">3.1. Access Control</a></li>
<li><a href="names.html#_accessibility-of-types-top-level-variables-and-function-declarations">3.2. Accessibility of Types, Top-Level Variables and Function Declarations</a>
<ul class="sectlevel3">
<li><a href="names.html#_accessibility-of-members">3.2.1. Accessibility of Members</a></li>
<li><a href="names.html#_valid-names">3.2.2. Valid Names</a></li>
<li><a href="names.html#_qualified-names">3.2.3. Qualified Names</a></li>
<li><a href="names.html#_name-duplicates">3.2.4. Name Duplicates</a>
<ul class="sectlevel4">
<li><a href="names.html#_lexical-environment">3.2.4.1. Lexical Environment</a></li>
<li><a href="names.html#_duplicates-and-shadowing">3.2.4.2. Duplicates and Shadowing</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
<li><a href="types.html#_types">4. Types</a>
<ul class="sectlevel2">
<li><a href="types.html#_overview">4.1. Overview</a></li>
<li><a href="types.html#_type-expressions">4.2. Type Expressions</a>
<ul class="sectlevel3">
<li><a href="types.html#_syntax">4.2.1. Syntax</a></li>
<li><a href="types.html#_properties">4.2.2. Properties</a></li>
<li><a href="types.html#_semantics">4.2.3. Semantics</a></li>
</ul>
</li>
<li><a href="types.html#_type-inference">4.3. Type Inference</a></li>
<li><a href="types.html#_generic-and-parameterized-types">4.4. Generic and Parameterized Types</a>
<ul class="sectlevel3">
<li><a href="types.html#_generic-types">4.4.1. Generic Types</a></li>
<li><a href="types.html#_type-variables">4.4.2. Type Variables</a></li>
<li><a href="types.html#_parameterized-types">4.4.3. Parameterized Types</a></li>
</ul>
</li>
<li><a href="types.html#_primitive-ecmascript-types">4.5. Primitive ECMAScript Types</a>
<ul class="sectlevel3">
<li><a href="types.html#_undefined-type">4.5.1. Undefined Type</a></li>
<li><a href="types.html#_null-type">4.5.2. Null Type</a></li>
<li><a href="types.html#_primitive-boolean-type">4.5.3. Primitive Boolean Type</a></li>
<li><a href="types.html#_primitive-string-type">4.5.4. Primitive String Type</a></li>
<li><a href="types.html#_primitive-number-type">4.5.5. Primitive Number Type</a></li>
<li><a href="types.html#_primitive-type-int">4.5.6. Primitive Type int</a></li>
<li><a href="types.html#_primitive-symbol-type">4.5.7. Primitive Symbol Type</a></li>
</ul>
</li>
<li><a href="types.html#_primitive-n4js-types">4.6. Primitive N4JS Types</a>
<ul class="sectlevel3">
<li><a href="types.html#_any-type">4.6.1. Any Type</a>
<ul class="sectlevel4">
<li><a href="types.html#any-type-semantics">4.6.1.1. Semantics</a></li>
<li><a href="types.html#any-type-type-inference">4.6.1.2. Type Inference</a>
<ul class="sectlevel5">
<li><a href="types.html#_default-type-of-variables">4.6.1.2.1. Default Type of Variables</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="types.html#_void-type">4.6.2. Void Type</a>
<ul class="sectlevel4">
<li><a href="types.html#void-type-semantics">4.6.2.1. Semantics</a></li>
</ul>
</li>
<li><a href="types.html#_unknown-type">4.6.3. Unknown Type</a></li>
<li><a href="types.html#_primitive-pathselector-and-i18nkey">4.6.4. Primitive Pathselector and I18nKey</a>
<ul class="sectlevel4">
<li><a href="types.html#pathselector-semantics">4.6.4.1. Semantics</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="types.html#_built-in-ecmascript-object-types">4.7. Built-in ECMAScript Object Types</a>
<ul class="sectlevel3">
<li><a href="types.html#ECMAScript-objects-semantics">4.7.1. Semantics</a></li>
<li><a href="types.html#_object-type">4.7.2. Object Type</a></li>
<li><a href="types.html#_function-object-type">4.7.3. Function-Object-Type</a></li>
<li><a href="types.html#_array-object-type">4.7.4. Array Object Type</a></li>
<li><a href="types.html#_string-object-type">4.7.5. String Object Type</a></li>
<li><a href="types.html#_boolean-object-type">4.7.6. Boolean Object Type</a></li>
<li><a href="types.html#_number-object-type">4.7.7. Number Object Type</a></li>
<li><a href="types.html#_global-object-type">4.7.8. Global Object Type</a></li>
<li><a href="types.html#_symbol">4.7.9. Symbol</a></li>
<li><a href="types.html#_promise">4.7.10. Promise</a></li>
<li><a href="types.html#_iterator-interface">4.7.11. Iterator Interface</a></li>
<li><a href="types.html#_iterable-interface">4.7.12. Iterable Interface</a></li>
</ul>
</li>
<li><a href="types.html#_built-in-n4js-types">4.8. Built-In N4JS Types</a>
<ul class="sectlevel3">
<li><a href="types.html#_n4object">4.8.1. N4Object</a>
<ul class="sectlevel4">
<li><a href="types.html#N4Object-semantics">4.8.1.1. Semantics</a></li>
</ul>
</li>
<li><a href="types.html#_n4class">4.8.2. N4Class</a></li>
<li><a href="types.html#IterableN">4.8.3. IterableN</a></li>
</ul>
</li>
<li><a href="types.html#_type-modifiers">4.9. Type Modifiers</a>
<ul class="sectlevel3">
<li><a href="types.html#Type_Modifiers_Dynamic">4.9.1. Dynamic</a></li>
<li><a href="types.html#_optional-return-types">4.9.2. Optional Return Types</a></li>
</ul>
</li>
<li><a href="types.html#_union-and-intersection-type-composed-types">4.10. Union and Intersection Type (Composed Types)</a>
<ul class="sectlevel3">
<li><a href="types.html#_union-type">4.10.1. Union Type</a>
<ul class="sectlevel4">
<li><a href="types.html#union-type-syntax">4.10.1.1. Syntax</a></li>
<li><a href="types.html#union-type-semantics">4.10.1.2. Semantics</a></li>
<li><a href="types.html#_warnings">4.10.1.3. Warnings</a></li>
</ul>
</li>
<li><a href="types.html#_intersection-type">4.10.2. Intersection Type</a>
<ul class="sectlevel4">
<li><a href="types.html#intersection-type-syntax">4.10.2.1. Syntax</a></li>
<li><a href="types.html#intersection-type-semantics">4.10.2.2. Semantics</a></li>
<li><a href="types.html#_warnings-2">4.10.2.3. Warnings</a></li>
</ul>
</li>
<li><a href="types.html#_composed-types-in-wildcards">4.10.3. Composed Types in Wildcards</a></li>
<li><a href="types.html#_property-access-for-composed-types">4.10.4. Property Access for Composed Types</a>
<ul class="sectlevel4">
<li><a href="types.html#_properties-of-union-type">4.10.4.1. Properties of Union Type</a>
<ul class="sectlevel5">
<li><a href="types.html#_remarks-on-union-type-s-members">4.10.4.1.1. Remarks on union type’s members:</a></li>
</ul>
</li>
<li><a href="types.html#_properties-of-intersection-type">4.10.4.2. Properties of Intersection Type</a>
<ul class="sectlevel5">
<li><a href="types.html#_remarks-on-intersection-type-s-methods">4.10.4.2.1. Remarks on intersection type’s methods:</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
<li><a href="types.html#_constructor-and-classifier-type">4.11. Constructor and Classifier Type</a>
<ul class="sectlevel3">
<li><a href="types.html#_syntax-3">4.11.1. Syntax</a></li>
<li><a href="types.html#_semantics-2">4.11.2. Semantics</a></li>
<li><a href="types.html#_constructors-and-prototypes-in-ecmascript-2015">4.11.3. Constructors and Prototypes in ECMAScript 2015</a></li>
</ul>
</li>
<li><a href="types.html#_this-type">4.12. This Type</a>
<ul class="sectlevel3">
<li><a href="types.html#this-type-syntax">4.12.1. Syntax</a></li>
<li><a href="types.html#this-keyword-semantics">4.12.2. Semantics</a></li>
</ul>
</li>
<li><a href="types.html#_enums">4.13. Enums</a>
<ul class="sectlevel3">
<li><a href="types.html#_enums-n4js">4.13.1. Enums (N4JS)</a>
<ul class="sectlevel4">
<li><a href="types.html#enums-syntax">4.13.1.1. Syntax</a></li>
<li><a href="types.html#enums-semantics">4.13.1.2. Semantics</a></li>
</ul>
</li>
<li><a href="types.html#_string-based-enums">4.13.2. String-Based Enums</a></li>
</ul>
</li>
<li><a href="types.html#_short-hand-syntax">4.14. Short-Hand Syntax</a>
<ul class="sectlevel3">
<li><a href="types.html#_array-short-hand-syntax">4.14.1. Array Short-Hand Syntax</a></li>
<li><a href="types.html#_iterablen-short-hand-syntax">4.14.2. IterableN Short-Hand Syntax</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="classifiers.html#_classifiers">5. Classifiers</a>
<ul class="sectlevel2">
<li><a href="classifiers.html#_n4js-specific-classifiers">5.1. N4JS Specific Classifiers</a>
<ul class="sectlevel3">
<li><a href="classifiers.html#_properties-2">5.1.1. Properties</a></li>
<li><a href="classifiers.html#_common-semantics-of-classifiers">5.1.2. Common Semantics of Classifiers</a></li>
<li><a href="classifiers.html#_classes">5.1.3. Classes</a>
<ul class="sectlevel4">
<li><a href="classifiers.html#_definition-of-classes">5.1.3.1. Definition of Classes</a>
<ul class="sectlevel5">
<li><a href="classifiers.html#class-syntax">5.1.3.1.1. Syntax</a></li>
<li><a href="classifiers.html#class-properties">5.1.3.1.2. Properties</a></li>
<li><a href="classifiers.html#class-type-inference">5.1.3.1.3. Type Inference</a></li>
</ul>
</li>
<li><a href="classifiers.html#class-semantics">5.1.3.2. Semantics</a></li>
<li><a href="classifiers.html#_final-modifier">5.1.3.3. Final Modifier</a></li>
<li><a href="classifiers.html#_abstract-classes">5.1.3.4. Abstract Classes</a></li>
<li><a href="classifiers.html#_non-instantiable-classes">5.1.3.5. Non-Instantiable Classes</a></li>
<li><a href="classifiers.html#_superclass">5.1.3.6. Superclass</a></li>
</ul>
</li>
<li><a href="classifiers.html#_interfaces">5.1.4. Interfaces</a>
<ul class="sectlevel4">
<li><a href="classifiers.html#_definition-of-interfaces">5.1.4.1. Definition of Interfaces</a>
<ul class="sectlevel5">
<li><a href="classifiers.html#interfaces-syntax">5.1.4.1.1. Syntax</a></li>
<li><a href="classifiers.html#interfaces-properties">5.1.4.1.2. Properties</a></li>
<li><a href="classifiers.html#interfaces-type-inference">5.1.4.1.3. Type Inference</a></li>
<li><a href="classifiers.html#interfaces-semantics">5.1.4.1.4. Semantics</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="classifiers.html#_generic-classifiers">5.1.5. Generic Classifiers</a></li>
<li><a href="classifiers.html#sec:definition-site-variance">5.1.6. Definition-Site Variance</a></li>
</ul>
</li>
<li><a href="classifiers.html#_members">5.2. Members</a>
<ul class="sectlevel3">
<li><a href="classifiers.html#_syntax-4">5.2.1. Syntax</a>
<ul class="sectlevel4">
<li><a href="classifiers.html#_properties-3">5.2.1.1. Properties</a></li>
</ul>
</li>
<li><a href="classifiers.html#_semantics-3">5.2.2. Semantics</a></li>
<li><a href="classifiers.html#_methods">5.2.3. Methods</a>
<ul class="sectlevel4">
<li><a href="classifiers.html#_syntax-5">5.2.3.1. Syntax</a></li>
<li><a href="classifiers.html#_properties-4">5.2.3.2. Properties</a></li>
<li><a href="classifiers.html#_semantics-4">5.2.3.3. Semantics</a></li>
<li><a href="classifiers.html#_final-methods">5.2.3.4. Final Methods</a></li>
<li><a href="classifiers.html#_abstract-methods">5.2.3.5. Abstract Methods</a></li>
<li><a href="classifiers.html#_generic-methods">5.2.3.6. Generic Methods</a></li>
</ul>
</li>
<li><a href="classifiers.html#_default-methods-in-interfaces">5.2.4. Default Methods in Interfaces</a>
<ul class="sectlevel4">
<li><a href="classifiers.html#_asynchronous-methods">5.2.4.1. Asynchronous Methods</a></li>
</ul>
</li>
<li><a href="classifiers.html#_constructors">5.2.5. Constructors</a>
<ul class="sectlevel4">
<li><a href="classifiers.html#_structural-this-type-in-constructor">5.2.5.1. Structural This Type in Constructor</a></li>
<li><a href="classifiers.html#spec-constructor">5.2.5.2. @Spec Constructor</a></li>
<li><a href="classifiers.html#_callable-constructors">5.2.5.3. Callable Constructors</a></li>
<li><a href="classifiers.html#_covariant-constructors">5.2.5.4. Covariant Constructors</a></li>
</ul>
</li>
<li><a href="classifiers.html#_data-fields">5.2.6. Data Fields</a>
<ul class="sectlevel4">
<li><a href="classifiers.html#data-fields-syntax">5.2.6.1. Syntax</a></li>
<li><a href="classifiers.html#data-fields-properties">5.2.6.2. Properties</a>
<ul class="sectlevel5">
<li><a href="classifiers.html#data-fields-semantics">5.2.6.2.1. Semantics</a></li>
<li><a href="classifiers.html#data-fields-type-inference">5.2.6.2.2. Type Inference</a></li>
</ul>
</li>
<li><a href="classifiers.html#_assignment-modifiers">5.2.6.3. Assignment Modifiers</a></li>
<li><a href="classifiers.html#_field-accessors-getter-setter">5.2.6.4. Field Accessors (Getter/Setter)</a>
<ul class="sectlevel5">
<li><a href="classifiers.html#field-acessors-syntax">5.2.6.4.1. Syntax</a></li>
<li><a href="classifiers.html#field-acessors-properties">5.2.6.4.2. Properties</a></li>
<li><a href="classifiers.html#field-accessors-semantics">5.2.6.4.3. Semantics</a></li>
</ul>
</li>
<li><a href="classifiers.html#optional-fields">5.2.6.5. Optional Fields</a>
<ul class="sectlevel5">
<li><a href="classifiers.html#_syntax-6">5.2.6.5.1. Syntax</a></li>
<li><a href="classifiers.html#_semantics-5">5.2.6.5.2. Semantics</a></li>
<li><a href="classifiers.html#_background">5.2.6.5.3. Background</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="classifiers.html#_static-members">5.2.7. Static Members</a>
<ul class="sectlevel4">
<li><a href="classifiers.html#_access-from-and-to-static-members">5.2.7.1. Access From and To Static Members</a></li>
<li><a href="classifiers.html#_generic-static-methods">5.2.7.2. Generic static methods</a></li>
<li><a href="classifiers.html#_static-members-of-interfaces">5.2.7.3. Static Members of Interfaces</a></li>
</ul>
</li>
<li><a href="classifiers.html#_redefinition-of-members">5.2.8. Redefinition of Members</a>
<ul class="sectlevel4">
<li><a href="classifiers.html#_overriding-of-members">5.2.8.1. Overriding of Members</a></li>
<li><a href="classifiers.html#_implementation-of-members">5.2.8.2. Implementation of Members</a>
<ul class="sectlevel5">
<li><a href="classifiers.html#_member-consumption">5.2.8.2.1. Member Consumption</a></li>
<li><a href="classifiers.html#_member-implementation">5.2.8.2.2. Member Implementation</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
<li><a href="classifiers.html#_structural-typing">5.3. Structural Typing</a>
<ul class="sectlevel3">
<li><a href="classifiers.html#_syntax-7">5.3.1. Syntax</a></li>
<li><a href="classifiers.html#_definition-site-structural-typing">5.3.2. Definition Site Structural Typing</a></li>
<li><a href="classifiers.html#_use-site-structural-typing">5.3.3. Use-Site Structural Typing</a></li>
<li><a href="classifiers.html#structural-readWriteInit-field-typing">5.3.4. Structural Read-only, Write-only and Initializer Field Typing</a></li>
<li><a href="classifiers.html#_public-setter-annotated-with-code-providesinitializer-code">5.3.5. Public Setter Annotated With <code>ProvidesInitializer</code></a></li>
<li><a href="classifiers.html#_structural-types-with-optional-fields">5.3.6. Structural Types With Optional Fields</a></li>
<li><a href="classifiers.html#_structural-types-with-access-modifier">5.3.7. Structural Types With Access Modifier</a></li>
<li><a href="classifiers.html#_structural-types-with-additional-members">5.3.8. Structural Types With Additional Members</a>
<ul class="sectlevel4">
<li><a href="classifiers.html#_syntax-8">5.3.8.1. Syntax</a>
<ul class="sectlevel5">
<li><a href="classifiers.html#_semantics-6">5.3.8.1.1. Semantics</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
<li><a href="functions.html#_functions">6. Functions</a>
<ul class="sectlevel2">
<li><a href="functions.html#_function-type">6.1. Function Type</a>
<ul class="sectlevel3">
<li><a href="functions.html#_properties-5">6.1.1. Properties</a></li>
<li><a href="functions.html#function-type-inference">6.1.2. Type Inference</a></li>
<li><a href="functions.html#_autoboxing-of-function-type">6.1.3. Autoboxing of Function Type</a></li>
<li><a href="functions.html#_arguments-object">6.1.4. Arguments Object</a></li>
</ul>
</li>
<li><a href="functions.html#_ecmascript-5-function-definition">6.2. ECMAScript 5 Function Definition</a>
<ul class="sectlevel3">
<li><a href="functions.html#_function-declaration">6.2.1. Function Declaration</a>
<ul class="sectlevel4">
<li><a href="functions.html#_syntax-9">6.2.1.1. Syntax</a></li>
<li><a href="functions.html#_semantics-8">6.2.1.2. Semantics</a></li>
</ul>
</li>
<li><a href="functions.html#_function-expression">6.2.2. Function Expression</a>
<ul class="sectlevel4">
<li><a href="functions.html#function-expression-syntax">6.2.2.1. Syntax</a></li>
<li><a href="functions.html#_semantics-and-type-inference">6.2.2.2. Semantics and Type Inference</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="functions.html#_ecmascript-2015-function-definition">6.3. ECMAScript 2015 Function Definition</a>
<ul class="sectlevel3">
<li><a href="functions.html#_formal-parameters">6.3.1. Formal Parameters</a>
<ul class="sectlevel4">
<li><a href="functions.html#Type_Modifiers_Optional">6.3.1.1. Optional Parameters</a></li>
<li><a href="functions.html#Type_Modifiers_Default">6.3.1.2. Default Parameters</a></li>
<li><a href="functions.html#Type_Modifiers_Variadic">6.3.1.3. Variadic</a></li>
</ul>
</li>
<li><a href="functions.html#_generator-functions">6.3.2. Generator Functions</a>
<ul class="sectlevel4">
<li><a href="functions.html#generator-functions-syntax">6.3.2.1. Syntax</a></li>
<li><a href="functions.html#generator-functions-semantics">6.3.2.2. Semantics</a></li>
<li><a href="functions.html#_generator-arrow-functions">6.3.2.3. Generator Arrow Functions</a></li>
</ul>
</li>
<li><a href="functions.html#_arrow-function-expression">6.3.3. Arrow Function Expression</a>
<ul class="sectlevel4">
<li><a href="functions.html#arrow-function-expression-syntax">6.3.3.1. Syntax</a></li>
<li><a href="functions.html#arrow-function-expression-semantics-and-type-inference">6.3.3.2. Semantics and Type Inference</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="functions.html#_ecmascript-proposals-function-definition">6.4. ECMAScript Proposals Function Definition</a>
<ul class="sectlevel3">
<li><a href="functions.html#_asynchronous-functions">6.4.1. Asynchronous Functions</a>
<ul class="sectlevel4">
<li><a href="functions.html#asynchronous-functions-syntax">6.4.1.1. Syntax</a></li>
<li><a href="functions.html#asynchronous-functions-semantics">6.4.1.2. Semantics</a></li>
<li><a href="functions.html#_asynchronous-arrow-functions">6.4.1.3. Asynchronous Arrow Functions</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="functions.html#_n4js-extended-function-definition">6.5. N4JS Extended Function Definition</a>
<ul class="sectlevel3">
<li><a href="functions.html#_generic-functions">6.5.1. Generic Functions</a></li>
<li><a href="functions.html#_promisifiable-functions">6.5.2. Promisifiable Functions</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="conversions_and_reflection.html#_conversions-and-reflection">7. Conversions and Reflection</a>
<ul class="sectlevel2">
<li><a href="conversions_and_reflection.html#_autoboxing-and-coercing">7.1. Autoboxing and Coercing</a>
<ul class="sectlevel3">
<li><a href="conversions_and_reflection.html#_coercing">7.1.1. Coercing</a></li>
<li><a href="conversions_and_reflection.html#_autoboxing-of-primitives">7.1.2. Autoboxing of Primitives</a></li>
<li><a href="conversions_and_reflection.html#_autoboxing-of-function-expressions-and-declarations">7.1.3. Autoboxing of Function Expressions and Declarations</a></li>
</ul>
</li>
<li><a href="conversions_and_reflection.html#_auto-conversion-of-objects">7.2. Auto-Conversion of Objects</a>
<ul class="sectlevel3">
<li><a href="conversions_and_reflection.html#_auto-conversion-of-class-instances">7.2.1. Auto-Conversion of Class Instances</a>
<ul class="sectlevel4">
<li><a href="conversions_and_reflection.html#_auto-conversion-of-interface-instances">7.2.1.1. Auto-Conversion of Interface Instances</a></li>
</ul>
</li>
<li><a href="conversions_and_reflection.html#_auto-conversion-of-enum-literals">7.2.2. Auto-Conversion of Enum Literals</a></li>
</ul>
</li>
<li><a href="conversions_and_reflection.html#_type-cast-and-type-check">7.3. Type Cast and Type Check</a>
<ul class="sectlevel3">
<li><a href="conversions_and_reflection.html#_type-cast">7.3.1. Type Cast</a></li>
<li><a href="conversions_and_reflection.html#_type-check">7.3.2. Type Check</a></li>
</ul>
</li>
<li><a href="conversions_and_reflection.html#_reflection-meta-information">7.4. Reflection meta-information</a>
<ul class="sectlevel3">
<li><a href="conversions_and_reflection.html#_reflection-for-classes">7.4.1. Reflection for Classes</a></li>
<li><a href="conversions_and_reflection.html#_reflection-for-interfaces">7.4.2. Reflection for Interfaces</a></li>
<li><a href="conversions_and_reflection.html#_reflection-for-enumerations">7.4.3. Reflection for Enumerations</a></li>
</ul>
</li>
<li><a href="conversions_and_reflection.html#_conversion-of-primitive-types">7.5. Conversion of primitive types</a></li>
</ul>
</li>
<li><a href="expressions.html#_expressions">8. Expressions</a>
<ul class="sectlevel2">
<li><a href="expressions.html#_ecmascript-5-expressions">8.1. ECMAScript 5 Expressions</a>
<ul class="sectlevel3">
<li><a href="expressions.html#_the-this-literal">8.1.1. The this Literal</a></li>
<li><a href="expressions.html#_identifier">8.1.2. Identifier</a></li>
<li><a href="expressions.html#_literals">8.1.3. Literals</a>
<ul class="sectlevel4">
<li><a href="expressions.html#_integer-literals">8.1.3.1. Integer Literals</a></li>
</ul>
</li>
<li><a href="expressions.html#_array-literal">8.1.4. Array Literal</a></li>
<li><a href="expressions.html#_object-literal">8.1.5. Object Literal</a>
<ul class="sectlevel4">
<li><a href="expressions.html#_properties-6">8.1.5.1. Properties</a></li>
<li><a href="expressions.html#_scoping-and-linking">8.1.5.2. Scoping and linking</a></li>
</ul>
</li>
<li><a href="expressions.html#_parenthesized-expression-and-grouping-operator">8.1.6. Parenthesized Expression and Grouping Operator</a></li>
<li><a href="expressions.html#_property-accessors">8.1.7. Property Accessors</a>
<ul class="sectlevel4">
<li><a href="expressions.html#properties-1">8.1.7.1. Properties</a></li>
</ul>
</li>
<li><a href="expressions.html#_new-expression">8.1.8. New Expression</a></li>
<li><a href="expressions.html#_function-expression-2">8.1.9. Function Expression</a></li>
<li><a href="expressions.html#_function-calls">8.1.10. Function Calls</a></li>
<li><a href="expressions.html#_postfix-expression">8.1.11. Postfix Expression</a></li>
<li><a href="expressions.html#_unary-expression">8.1.12. Unary Expression</a></li>
<li><a href="expressions.html#_multiplicative-expression">8.1.13. Multiplicative Expression</a></li>
<li><a href="expressions.html#_additive-expression">8.1.14. Additive Expression</a>
<ul class="sectlevel4">
<li><a href="expressions.html#type-inference-10">8.1.14.1. Type Inference</a></li>
</ul>
</li>
<li><a href="expressions.html#_bitwise-shift-expression">8.1.15. Bitwise Shift Expression</a></li>
<li><a href="expressions.html#_relational-expression">8.1.16. Relational Expression</a></li>
<li><a href="expressions.html#_equality-expression">8.1.17. Equality Expression</a></li>
<li><a href="expressions.html#_binary-bitwise-expression">8.1.18. Binary Bitwise Expression</a></li>
<li><a href="expressions.html#_binary-logical-expression">8.1.19. Binary Logical Expression</a></li>
<li><a href="expressions.html#_conditional-expression">8.1.20. Conditional Expression</a></li>
<li><a href="expressions.html#_assignment-expression">8.1.21. Assignment Expression</a></li>
<li><a href="expressions.html#_comma-expression">8.1.22. Comma Expression</a></li>
</ul>
</li>
<li><a href="expressions.html#_ecmascript-6-expressions">8.2. ECMAScript 6 Expressions</a>
<ul class="sectlevel3">
<li><a href="expressions.html#_the-super-keyword">8.2.1. The super Keyword</a></li>
</ul>
</li>
<li><a href="expressions.html#_ecmascript-7-expressions">8.3. ECMAScript 7 Expressions</a>
<ul class="sectlevel3">
<li><a href="expressions.html#_await-expression">8.3.1. Await Expression</a></li>
</ul>
</li>
<li><a href="expressions.html#_n4js-specific-expressions">8.4. N4JS Specific Expressions</a>
<ul class="sectlevel3">
<li><a href="expressions.html#_class-expression">8.4.1. Class Expression</a></li>
<li><a href="expressions.html#_cast-as-expression">8.4.2. Cast (As) Expression</a>
<ul class="sectlevel4">
<li><a href="expressions.html#cast-as-expression-semantics-type-inference">8.4.2.1. Semantics and Type Inference</a></li>
</ul>
</li>
<li><a href="expressions.html#Import_Calls">8.4.3. Import Calls</a></li>
</ul>
</li>
<li><a href="expressions.html#compile-time-expressions">8.5. Compile-Time Expressions</a></li>
</ul>
</li>
<li><a href="statements.html#_statements">9. Statements</a>
<ul class="sectlevel2">
<li><a href="statements.html#_ecmascript-5-statements">9.1. ECMAScript 5 Statements</a>
<ul class="sectlevel3">
<li><a href="statements.html#_function-or-field-accessor-bodies">9.1.1. Function or Field Accessor Bodies</a></li>
<li><a href="statements.html#_variable-statement">9.1.2. Variable Statement</a></li>
<li><a href="statements.html#_if-statement">9.1.3. If Statement</a></li>
<li><a href="statements.html#_iteration-statements">9.1.4. Iteration Statements</a></li>
<li><a href="statements.html#_return-statement">9.1.5. Return Statement</a></li>
<li><a href="statements.html#_with-statement">9.1.6. With Statement</a></li>
<li><a href="statements.html#_switch-statement">9.1.7. Switch Statement</a></li>
<li><a href="statements.html#_throw-try-and-catch-statements">9.1.8. Throw, Try, and Catch Statements</a></li>
<li><a href="statements.html#_debugger-statement">9.1.9. Debugger Statement</a></li>
</ul>
</li>
<li><a href="statements.html#_ecmascript-6-statements">9.2. ECMAScript 6 Statements</a>
<ul class="sectlevel3">
<li><a href="statements.html#_let">9.2.1. Let</a></li>
<li><a href="statements.html#_const">9.2.2. Const</a></li>
<li><a href="statements.html#_for-of-statement">9.2.3. <code>for &#8230;&#8203; of</code> statement</a></li>
<li><a href="statements.html#_import-statement">9.2.4. Import Statement</a>
<ul class="sectlevel4">
<li><a href="statements.html#Dynamic_Imports">9.2.4.1. Dynamic Imports</a></li>
<li><a href="statements.html#_immutabilaty-of-imports">9.2.4.2. Immutabilaty of Imports</a></li>
</ul>
</li>
<li><a href="statements.html#_export-statement">9.2.5. Export Statement</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="annotations.html#_annotations">10. Annotations</a>
<ul class="sectlevel2">
<li><a href="annotations.html#_introduction-2">10.1. Introduction</a>
<ul class="sectlevel3">
<li><a href="annotations.html#_syntax-13">10.1.1. Syntax</a></li>
<li><a href="annotations.html#_properties-7">10.1.2. Properties</a></li>
<li><a href="annotations.html#_element-specific-annotations">10.1.3. Element-Specific Annotations</a></li>
<li><a href="annotations.html#_general-annotations">10.1.4. General Annotations</a>
<ul class="sectlevel4">
<li><a href="annotations.html#_idebug">10.1.4.1. IDEBUG</a></li>
</ul>
</li>
<li><a href="annotations.html#idebug-syntax">10.1.5. Syntax</a>
<ul class="sectlevel4">
<li><a href="annotations.html#_semantics-11">10.1.5.1. Semantics</a></li>
<li><a href="annotations.html#_suppress-warnings">10.1.5.2. Suppress Warnings</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="annotations.html#_declaration-of-annotations">10.2. Declaration of Annotations</a></li>
</ul>
</li>
<li><a href="extended_fetaures.html#_extended-fetaures">11. Extended Fetaures</a>
<ul class="sectlevel2">
<li><a href="extended_fetaures.html#_array-and-object-destructuring">11.1. Array and Object Destructuring</a>
<ul class="sectlevel3">
<li><a href="extended_fetaures.html#_syntax-14">11.1.1. Syntax</a></li>
<li><a href="extended_fetaures.html#_semantics-12">11.1.2. Semantics</a></li>
</ul>
</li>
<li><a href="extended_fetaures.html#_dependency-injection">11.2. Dependency Injection</a>
<ul class="sectlevel3">
<li><a href="extended_fetaures.html#_di-components-and-injectors">11.2.1. DI Components and Injectors</a>
<ul class="sectlevel4">
<li><a href="extended_fetaures.html#_dicomponent-relations">11.2.1.1. DIComponent Relations</a></li>
</ul>
</li>
<li><a href="extended_fetaures.html#_binders-and-bindings">11.2.2. Binders and Bindings</a></li>
<li><a href="extended_fetaures.html#_injection-points">11.2.3. Injection Points</a>
<ul class="sectlevel4">
<li><a href="extended_fetaures.html#_field-injection">11.2.3.1. Field Injection</a></li>
<li><a href="extended_fetaures.html#_constructor-injection">11.2.3.2. Constructor Injection</a></li>
<li><a href="extended_fetaures.html#_method-injection">11.2.3.3. Method Injection</a>
<ul class="sectlevel5">
<li><a href="extended_fetaures.html#_provider">11.2.3.3.1. Provider</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="extended_fetaures.html#_n4js-di-life-cycle-and-scopes">11.2.4. N4JS DI Life Cycle and Scopes</a>
<ul class="sectlevel4">
<li><a href="extended_fetaures.html#_injection-cylces">11.2.4.1. Injection Cylces</a></li>
<li><a href="extended_fetaures.html#_default-scope">11.2.4.2. Default Scope</a></li>
<li><a href="extended_fetaures.html#_singleton-scope">11.2.4.3. Singleton Scope</a></li>
<li><a href="extended_fetaures.html#_per-injection-chain-singleton">11.2.4.4. Per Injection Chain Singleton</a></li>
</ul>
</li>
<li><a href="extended_fetaures.html#_validation-of-callsites-targeting-n4injector-methods">11.2.5. Validation of callsites targeting N4Injector methods</a></li>
<li><a href="extended_fetaures.html#_n4js-di-annotations">11.2.6. N4JS DI Annotations</a>
<ul class="sectlevel4">
<li><a href="extended_fetaures.html#_n4js-di-generateinjector">11.2.6.1. N4JS DI @GenerateInjector</a></li>
<li><a href="extended_fetaures.html#_n4js-di-withparentinjector">11.2.6.2. N4JS DI @WithParentInjector</a></li>
<li><a href="extended_fetaures.html#_n4js-di-usebinder">11.2.6.3. N4JS DI @UseBinder</a></li>
<li><a href="extended_fetaures.html#_n4js-di-binder">11.2.6.4. N4JS DI @Binder</a></li>
<li><a href="extended_fetaures.html#_n4js-di-bind">11.2.6.5. N4JS DI @Bind</a></li>
<li><a href="extended_fetaures.html#_n4js-di-provides">11.2.6.6. N4JS DI @Provides</a></li>
<li><a href="extended_fetaures.html#_n4js-di-inject">11.2.6.7. N4JS DI @Inject</a></li>
<li><a href="extended_fetaures.html#_n4js-di-singleton">11.2.6.8. N4JS DI @Singleton</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="extended_fetaures.html#_test-support">11.3. Test Support</a></li>
<li><a href="extended_fetaures.html#_polyfill-definitions">11.4. Polyfill Definitions</a>
<ul class="sectlevel3">
<li><a href="extended_fetaures.html#_runtime-polyfill-definitions">11.4.1. Runtime Polyfill Definitions</a></li>
<li><a href="extended_fetaures.html#_static-polyfill-definitions">11.4.2. Static Polyfill Definitions</a></li>
<li><a href="extended_fetaures.html#_transpiling-static-polyfilled-classes">11.4.3. Transpiling static polyfilled classes</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="components.html#_components">12. Components</a>
<ul class="sectlevel2">
<li><a href="components.html#_overview-2">12.1. Overview</a></li>
<li><a href="components.html#Component_Types">12.2. Component Types</a>
<ul class="sectlevel3">
<li><a href="components.html#_libraries">12.2.1. Libraries</a></li>
<li><a href="components.html#_runtime-environment-and-runtime-libraries">12.2.2. Runtime Environment and Runtime Libraries</a></li>
<li><a href="components.html#_tests">12.2.3. Tests</a></li>
<li><a href="components.html#_type-definitions">12.2.4. Type Definitions</a></li>
</ul>
</li>
<li><a href="components.html#package-json">12.3. Package.json File</a>
<ul class="sectlevel3">
<li><a href="components.html#_basic-properties">12.3.1. Basic Properties</a></li>
<li><a href="components.html#_n4js-properties">12.3.2. N4JS Properties</a></li>
<li><a href="components.html#_constraints">12.3.3. Constraints</a></li>
</ul>
</li>
<li><a href="components.html#_support-for-npm-scopes">12.4. Support for NPM Scopes</a></li>
<li><a href="components.html#sec:N4JS-Type-Definitions">12.5. N4JS Type Definitions</a>
<ul class="sectlevel3">
<li><a href="components.html#_specify-type-definition">12.5.1. Specify Type Definition</a></li>
<li><a href="components.html#_name-conventions">12.5.2. Name Conventions</a></li>
<li><a href="components.html#_version-conventions">12.5.3. Version Conventions</a>
<ul class="sectlevel4">
<li><a href="components.html#_define-a-new-type-definition-package">12.5.3.1. Define a New Type Definition Package</a></li>
<li><a href="components.html#_using-a-type-definition-package">12.5.3.2. Using a Type Definition Package</a></li>
<li><a href="components.html#_rational">12.5.3.3. Rational</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="components.html#_modules">12.6. Modules</a></li>
<li><a href="components.html#_api-and-implementation-component">12.7. API and Implementation Component</a>
<ul class="sectlevel3">
<li><a href="components.html#_execution-of-api-and-implementation-components">12.7.1. Execution of API and Implementation Components</a></li>
<li><a href="components.html#_api-and-implementation-with-di">12.7.2. API and Implementation With DI</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="plainjs.html#_plainjs">13. PlainJS</a>
<ul class="sectlevel2">
<li><a href="plainjs.html#_type-inference-and-validation-for-plain-js">13.1. Type Inference and Validation for Plain JS</a></li>
<li><a href="plainjs.html#_external-declarations">13.2. External Declarations</a>
<ul class="sectlevel3">
<li><a href="plainjs.html#_declaring-externals">13.2.1. Declaring externals</a></li>
<li><a href="plainjs.html#_instantiating-external-classes">13.2.2. Instantiating external classes</a></li>
<li><a href="plainjs.html#_implementation-of-external-declarations">13.2.3. Implementation of External Declarations</a></li>
<li><a href="plainjs.html#_example">13.2.4. Example</a></li>
</ul>
</li>
<li><a href="plainjs.html#_global-definitions">13.3. Global Definitions</a></li>
<li><a href="plainjs.html#_runtime-definitions">13.4. Runtime Definitions</a></li>
<li><a href="plainjs.html#_applying-polyfills">13.5. Applying Polyfills</a></li>
</ul>
</li>
<li><a href="jsdoc.html#_jsdoc-2">14. JSDoc</a>
<ul class="sectlevel2">
<li><a href="jsdoc.html#_general-n4jsdoc-features">14.1. General N4JSDoc Features</a>
<ul class="sectlevel3">
<li><a href="jsdoc.html#_provided-inline-tags">14.1.1. Provided Inline Tags</a>
<ul class="sectlevel4">
<li><a href="jsdoc.html#jsdoc_tag__code">14.1.1.1. @code</a></li>
<li><a href="jsdoc.html#jsdoc_tag__link">14.1.1.2. @link</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="jsdoc.html#_n4jsdoc-for-user-projects">14.2. N4JSdoc for User Projects</a>
<ul class="sectlevel3">
<li><a href="jsdoc.html#_standard-tags">14.2.1. Standard Tags</a>
<ul class="sectlevel4">
<li><a href="jsdoc.html#_-author">14.2.1.1. @author</a></li>
<li><a href="jsdoc.html#jsdoc_tag_param">14.2.1.2. @param</a></li>
<li><a href="jsdoc.html#jsdoc_tag_return">14.2.1.3. @return</a></li>
</ul>
</li>
<li><a href="jsdoc.html#_test-related-tags">14.2.2. Test Related Tags</a>
<ul class="sectlevel4">
<li><a href="jsdoc.html#jsdoc_tag__testee">14.2.2.1. @testee</a></li>
<li><a href="jsdoc.html#jsdoc_tag__testeeFromType">14.2.2.2. @testeeFromType</a></li>
<li><a href="jsdoc.html#_testeeType_and__testeeMember">14.2.2.3. @testeeType and @testeeMember</a></li>
<li><a href="jsdoc.html#jsdoc_tag_reqid_in_Tests">14.2.2.4. @reqid in Tests</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="jsdoc.html#_n4jsdoc-for-api-and-implementation-projects">14.3. N4JSDoc for API and Implementation Projects</a>
<ul class="sectlevel3">
<li><a href="jsdoc.html#jsdoc_tag__apiNote">14.3.1. @apiNote</a></li>
<li><a href="jsdoc.html#API_Project_Tags">14.3.2. API Project Tags</a>
<ul class="sectlevel4">
<li><a href="jsdoc.html#jsdoc_tag_apiState">14.3.2.1. @apiState</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
<li><a href="jsx.html#_jsx">15. JSX</a>
<ul class="sectlevel2">
<li><a href="jsx.html#_jsx-support">15.1. JSX Support</a></li>
<li><a href="jsx.html#_jsx-backend">15.2. JSX Backend</a></li>
</ul>
</li>
<li><a href="grammars.html#_grammars">16. Grammars</a>
<ul class="sectlevel2">
<li><a href="grammars.html#_type-expressions-grammar">16.1. Type Expressions Grammar</a></li>
<li><a href="grammars.html#_n4js-language-grammar">16.2. N4JS Language Grammar</a></li>
</ul>
</li>
<li><a href="jsobjects.html#_jsobjects">17. JSObjects</a>
<ul class="sectlevel2">
<li><a href="jsobjects.html#_object">17.1. Object</a></li>
<li><a href="jsobjects.html#_string">17.2. String</a></li>
<li><a href="jsobjects.html#_boolean">17.3. Boolean</a></li>
<li><a href="jsobjects.html#_number">17.4. Number</a>
<ul class="sectlevel3">
<li><a href="jsobjects.html#_static-attributes">17.4.1. Static Attributes</a></li>
</ul>
</li>
<li><a href="jsobjects.html#function">17.5. Function</a></li>
<li><a href="jsobjects.html#_error">17.6. Error</a></li>
<li><a href="jsobjects.html#_array">17.7. Array</a></li>
<li><a href="jsobjects.html#_date">17.8. Date</a></li>
<li><a href="jsobjects.html#_math">17.9. Math</a>
<ul class="sectlevel3">
<li><a href="jsobjects.html#static-attributes-1">17.9.1. Static Attributes</a></li>
</ul>
</li>
<li><a href="jsobjects.html#_regexp">17.10. RegExp</a></li>
<li><a href="jsobjects.html#_json">17.11. JSON</a></li>
</ul>
</li>
<li><a href="n4js_objects.html#_n4js-objects">18. N4JS Objects</a>
<ul class="sectlevel2">
<li><a href="n4js_objects.html#_reflection-model">18.1. Reflection Model</a></li>
<li><a href="n4js_objects.html#_error-types">18.2. Error Types</a>
<ul class="sectlevel3">
<li><a href="n4js_objects.html#_n4apinotimplemented">18.2.1. N4ApiNotImplemented</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="appendix_a_acronyms.html#_acronyms">Appendix A: Acronyms</a></li>
<li><a href="appendix_b_license.html#sec:License">Appendix B: License</a></li>
<li><a href="appendix_c_bibliography.html#_bibliography">Appendix C: Bibliography</a></li>
</ul>
</div>
</div>
<div id="content"><div class="sect1">
<h2 id="_introduction"><a class="anchor" href="#_introduction"></a><a class="link" href="#_introduction">1. Introduction</a></h2>
<div class="sectionbody">
<div class="paragraph">
<p>This specification defines the N4JS language.</p>
</div>
<div class="paragraph">
<p>In general, the N4JS JavaScript dialect used is identical to the standard ECMAScript as defined in the 6th edition of
ECMA-262, also known as ECMAScript 2015, referred to as [<a href="appendix_c_bibliography.html#ECMA15a">ECMA15a</a>].</p>
</div>
<div class="sect2 language-n4js">
<h3 id="_notation"><a class="anchor" href="#_notation"></a><a class="link" href="#_notation">1.1. Notation</a></h3>
<div class="sect3">
<h4 id="_grammar-notation"><a class="anchor" href="#_grammar-notation"></a><a class="link" href="#_grammar-notation">1.1.1. Grammar Notation</a></h4>
<div class="paragraph">
<p>For the specification of the syntax and structure of elements, we use a
slightly augmented similar to the grammar language of Xtext <a href="http://www.eclipse.org/Xtext/documentation/301_grammarlanguage.html">Grammar Language</a>.</p>
</div>
<div class="paragraph">
<p>Similar to [<a href="appendix_c_bibliography.html#ECMA11a">ECMA11a</a>], we define types with properties only for the purpose of explanation and usage within this specification.
We use the Xtext notation style to assign values to meta-properties.
Particularly, we use the Xtext notation for collection (<code>+=</code>) and boolean (<code>?=</code>) values.
These properties are written in italics. Enumerations are defined similar to Xtext.
In order to allow the specification of default values, which are often defined by omitting the value, we always define the literal explicitly if it can be defined by the user.</p>
</div>
<div class="paragraph">
<p>The following lists informally defines the grammar:</p>
</div>
<div class="dlist">
<dl>
<dt class="hdlist1">Terminal</dt>
<dd>
<p>Terminals (or terminal strings) are enclosed in single quotes, e.g., <code>terminal</code>.</p>
</dd>
<dt class="hdlist1">Enumerations</dt>
<dd>
<p>Rules which contain only terminals used as values for properties are
marked with <code>enum</code> for enumeration.</p>
</dd>
<dt class="hdlist1">Properties</dt>
<dd>
<p>Values of non-terminals, e.g., other rules, can be assigned to
properties. The property name and the assignment are not part of the
original syntax and only used for the meta description. E.g., <code><em>name=</em>Identifier</code>.</p>
</dd>
<dt class="hdlist1">Collection Properties</dt>
<dd>
<p>If a property is a collection, values are added to that list via <code>+=</code>.
E.g.,<code><em>property+=</em>Value</code> .</p>
</dd>
<dt class="hdlist1">Boolean Properties</dt>
<dd>
<p>Boolean properties are set to false by default, if the value (usually
a terminal) is found, the boolean value is set to true. Often, the
name of the property is similar to the terminal. E.g., <code><em>final?</em>='final'?</code>.</p>
</dd>
</dl>
</div>
<div class="paragraph">
<p>Properties of a non-terminal are sometimes listed again below the
grammar. In that case, often pseudo properties are introduced which are
derived from other properties and which are only used for
simplification.</p>
</div>
</div>
<div class="sect3">
<h4 id="_type-judgments-and-rules-and-constraints-notation"><a class="anchor" href="#_type-judgments-and-rules-and-constraints-notation"></a><a class="link" href="#_type-judgments-and-rules-and-constraints-notation">1.1.2. Type Judgments and Rules and Constraints Notation</a></h4>
<div class="sect4">
<h5 id="_typing-rules-and-judgments"><a class="anchor" href="#_typing-rules-and-judgments"></a><a class="link" href="#_typing-rules-and-judgments">1.1.2.1. Typing Rules and Judgments</a></h5>
<div class="openblock definition">
<div class="content">
<div class="paragraph">
<p><a id="rule"></a><strong>Definition:</strong> <a href="#rule">Rule</a></p>
</div>
<div class="paragraph">
<p>We use the common notation for rules such as type inference rules <sup class="footnote">[<a id="_footnoteref_1" class="footnote" href="appendix_c_bibliography.html#_footnote_1" title="View footnote.">1</a>]</sup>, that is</p>
</div>
<div class="openblock">
<div class="content">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><mi>p</mi><mi>r</mi><mi>e</mi><mi>m</mi><mi>i</mi><mi>s</mi><mi>e</mi><mi>s</mi></mrow><mrow><mi>c</mi><mi>o</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>u</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow></mfrac><mspace width="5.0mm"/><mstyle mathvariant="normal"><mtext>rule name</mtext></mstyle></math>
</div>
</div>
<div class="paragraph">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>r</mi><mi>e</mi><mi>m</mi><mi>i</mi><mi>s</mi><mi>e</mi><mi>s</mi></math> is the rule’s premises (e.g., the expression to be inferred), <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>u</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></math> the result of the rule.
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mi>u</mi><mi>l</mi><mi>e</mi><mi>n</mi><mi>a</mi><mi>m</mi><mi>e</mi></math> is an optional condition which may be omitted.</p>
</div>
<div class="paragraph">
<p>Both parts of the rule may contain multiple expressions, which are concatenated via 'and'.</p>
</div>
<div class="paragraph">
<p>For example, the following</p>
</div>
<div class="openblock">
<div class="content">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><msub><mi>P</mi><mn>1</mn></msub><mspace width="5.0mm"/><msub><mi>P</mi><mn>2</mn></msub><mspace width="5.0mm"/><msub><mi>P</mi><mn>3</mn></msub></mrow><mi>C</mi></mfrac></math>
</div>
</div>
<div class="paragraph">
<p>can be read as</p>
</div>
<div class="quoteblock">
<blockquote>
if <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>1</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>2</mn></msub></math>, <em>and</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>3</mn></msub></math> are all true, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> is true as well.
</blockquote>
</div>
</div>
</div>
<div class="paragraph">
<p>The following judgments (with relation symbols) are used:</p>
</div>
<div class="dlist">
<dl>
<dt class="hdlist1">subtype <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&lt;</mo></math> </dt>
<dd>
<p>-</p>
</dd>
<dt class="hdlist1">type <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathvariant="monospace"><mtext>:</mtext></mstyle></math> </dt>
<dd>
<p>in which the left hand side is a declaration or expression, and the right hand side a type.
We also use <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>[</mo><mspace width="-0.167em"/><mrow><mo>[</mo></mrow></mrow><mrow><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/></mrow><mrow><mrow><mo>]</mo></mrow><mspace width="-0.167em"/><mo>]</mo></mrow></math> as a function returning the (inferred) type of an expression.</p>
</dd>
<dt class="hdlist1">expectedTypeIn <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⊲</mo><mi>:</mi></math> </dt>
<dd>
<p>a relation with three arguments:
  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>e</mi><mi>r</mi><mo>⊲</mo><mi>e</mi><mi>x</mi><mi>p</mi><mi>r</mi><mi>e</mi><mi>s</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>:</mi><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi></math> means, that
  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>x</mi><mi>p</mi><mi>r</mi><mi>e</mi><mi>s</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></math> is expected to be a subtype of
  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi></math> inside <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>e</mi><mi>r</mi></math></p>
</dd>
</dl>
</div>
<div class="paragraph">
<p>The following statement, for example, defines transitivity of subtypes
(in a simplified manner):</p>
</div>
<div class="openblock">
<div class="content">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><mi>Γ</mi><mo>⊢</mo><mi>B</mi><mspace width="1.0mm"/><mo>&lt;</mo><mstyle mathvariant="monospace"><mtext>:</mtext></mstyle><mspace width="1.0mm"/><mi>A</mi><mspace width="5.0mm"/><mi>Γ</mi><mo>⊢</mo><mi>C</mi><mspace width="1.0mm"/><mo>&lt;</mo><mstyle mathvariant="monospace"><mtext>:</mtext></mstyle><mspace width="1.0mm"/><mi>B</mi></mrow><mrow><mi>Γ</mi><mo>⊢</mo><mi>C</mi><mspace width="1.0mm"/><mo>&lt;</mo><mstyle mathvariant="monospace"><mtext>:</mtext></mstyle><mspace width="1.0mm"/><mi>A</mi></mrow></mfrac></math>
</div>
</div>
<div class="paragraph">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⊢</mo></math> is the context containing (bound) type variables etc., <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⊢</mo></math> can be read as <code>entails</code>.
Thus, the rule can be read as follows:</p>
</div>
<div class="quoteblock">
<blockquote>
if the type B is a subtype of type A in context <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Γ</mi></math> (i.e. with constraints on type variables specified in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Γ</mi></math>), and if type C is a subtype of B, then C is also a subtype of A in context <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Γ</mi></math>.
</blockquote>
</div>
<div class="paragraph">
<p>In rules, we sometimes omit the environment if it is not needed.
New information is sometimes added to the environment, in particular, substitutions (that is binding type variables to a type).
The set of substitutions is written with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> (theta).
If new substitutions are explicitly added to that set, we write <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mfenced close=")" open="("><mrow><mi>V</mi><mo>←</mo><mi>T</mi></mrow></mfenced></math> (<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> is substituted with type <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>).
Often, these bindings are computed from a parameterized type reference which declares type arguments which are bound to the type variables of the generic declaration.
In this case we simply write <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mfenced close=")" open="("><mi>p</mi></mfenced></math>, in which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> is the parameterized type declaration.
As these new substitutions must become part of a (newly) created environment, we then usually write <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Γ</mi><mo>←</mo><mi>θ</mi><mfenced close=")" open="("><mi>p</mi></mfenced></math>.
These substitutions are usually omitted.</p>
</div>
</div>
<div class="sect4">
<h5 id="_types-of-an-element"><a class="anchor" href="#_types-of-an-element"></a><a class="link" href="#_types-of-an-element">1.1.2.2. Types of an Element</a></h5>
<div class="paragraph">
<p>A variable or other typed element may be associated with three types:</p>
</div>
<div class="olist arabic">
<ol class="arabic">
<li>
<p>Declared type: the type explicitly specified in the code, e.g., <code>var s: string</code>.</p>
</li>
<li>
<p>Inferred type: the type inferred by the type inferencer, e.g., <code>var s = "Hello"</code> infers the type of s to <code>string</code>. I.e.
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Γ</mi><mo>⊢</mo><mi>s</mi><mi>:</mi><mrow><mi>s</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>n</mi><mi>g</mi></mrow></math> will be true, or <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>[</mo><mspace width="-0.167em"/><mrow><mo>[</mo></mrow></mrow><mi>s</mi><mrow><mrow><mo>]</mo></mrow><mspace width="-0.167em"/><mo>]</mo></mrow><mspace width="1.0mm"/><mo>&lt;</mo><mstyle mathvariant="monospace"><mtext>:</mtext></mstyle><mspace width="1.0mm"/><mi>s</mi><mi>t</mi><mi>r</mi><mi>i</mi><mi>n</mi><mi>g</mi></math>.
If an element is annotated with a type ,i.e. it has a declared type, the inferred type will always be the declared type.</p>
</li>
<li>
<p>Actual type: the actual type of a variable during runtime.
This type information is not available at compile time and ignored in this specification.</p>
</li>
</ol>
</div>
<div class="paragraph">
<p>These types are not type declarations but type references, in fact, as they may be parameterized.
For the sake of simplicity, we often omit the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>e</mi><mi>f</mi></math> suffix to shorten formulas.
Consequently, we define the following properties and pseudo properties for typed elements such as variables:</p>
</div>
<div class="dlist">
<dl>
<dt class="hdlist1">declaredType<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>e</mi><mi>f</mi></math> </dt>
<dd>
<p>The explicitly declared type, this is usually a real property of the construct.
Not all elements allow the specification of a declared type, such as expressions.</p>
</dd>
<dt class="hdlist1">inferredType<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>e</mi><mi>f</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>[</mo><mspace width="-0.167em"/><mrow><mo>[</mo></mrow></mrow><mrow><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/></mrow><mrow><mrow><mo>]</mo></mrow><mspace width="-0.167em"/><mo>]</mo></mrow></math></dt>
<dd>
<p>This pseudo property is the inferred type computed by the type inferencer.</p>
</dd>
<dt class="hdlist1">type<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>e</mi><mi>f</mi></math> </dt>
<dd>
<p>A pseudo property for elements with a <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>e</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi></math> property.
It is similar to the inferred type, i.e. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>.</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>=</mo><mrow><mo>[</mo><mspace width="-0.167em"/><mrow><mo>[</mo></mrow></mrow><mi>e</mi><mrow><mrow><mo>]</mo></mrow><mspace width="-0.167em"/><mo>]</mo></mrow></math></p>
</dd>
</dl>
</div>
</div>
</div>
</div>
<div class="sect2 language-n4js">
<h3 id="_auxiliary-functions"><a class="anchor" href="#_auxiliary-functions"></a><a class="link" href="#_auxiliary-functions">1.2. Auxiliary Functions</a></h3>
<div class="paragraph">
<p>This section describes some auxiliary functions required for definition of type inference rules later on.</p>
</div>
<div class="sect3">
<h4 id="_binding"><a class="anchor" href="#_binding"></a><a class="link" href="#_binding">1.2.1. Binding</a></h4>
<div class="paragraph">
<p>Binding an identifier (variable reference) to a variable declaration (or
variable definition) is not part of this specification as this is
standard ECMAScript functionality. However, some valid ECMAScript
bindings are permitted due to visibility constraints.</p>
</div>
<div class="openblock definition">
<div class="content">
<div class="paragraph">
<p><a id="binding_relation"></a><strong>Definition:</strong> <a href="#binding_relation">Binding Relation</a></p>
</div>
<div class="paragraph">
<p>We define a pseudo relation</p>
</div>
<div class="openblock">
<div class="content">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>b</mi><mi>i</mi><mi>n</mi><mi>d</mi><mi>:</mi><mi>V</mi><mi>a</mi><mi>r</mi><mi>i</mi><mi>a</mi><mi>b</mi><mi>l</mi><mi>e</mi><mi>R</mi><mi>e</mi><mi>f</mi><mi>e</mi><mi>r</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>e</mi><mo>×</mo><mi>V</mi><mi>a</mi><mi>r</mi><mi>i</mi><mi>a</mi><mi>b</mi><mi>l</mi><mi>e</mi><mi>D</mi><mi>e</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math>
</div>
</div>
<div class="paragraph">
<p>which binds a reference, i.e. an identifier, to a declaration (e.g.,variable declaration).</p>
</div>
<div class="paragraph">
<p>Binding of variable references to declaration is defined by ECMAScript already.
Type references only occur in type expressions, how these are handled is explained in <a href="types.html#_type-expressions">Type Expressions</a>.</p>
</div>
<div class="paragraph">
<p>We usually omit this binding mechanism in most rules and use the reference similarly to the declaration or definition it is bound to.
If a variable reference <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, for example, is bound to a variable declaration <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math>, i.e. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mi>i</mi><mi>n</mi><mi>d</mi><mfenced close=")" open="("><mi>r</mi><mi>D</mi></mfenced></math>, we simply write <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>.</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi></math> instead of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mi>i</mi><mi>n</mi><mi>d</mi><mfenced close=")" open="("><mi>r</mi><mi>D</mi></mfenced><mo>,</mo><mi>D</mi><mo>.</mo><mi>t</mi><mi>y</mi><mi>p</mi><mi>e</mi></math> to refer to the type expression
(of the variable).<sup class="footnote">[<a id="_footnoteref_2" class="footnote" href="appendix_c_bibliography.html#_footnote_2" title="View footnote.">2</a>]</sup></p>
</div>
</div>
</div>
<div class="paragraph">
<p>A <code>DeclaredType</code> references the type declaration by its simple name that has been imported from a module specifier.
We define the method <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mi>i</mi><mi>n</mi><mi>d</mi></math> for declared types as well:</p>
</div>
<div class="openblock definition">
<div class="content">
<div class="paragraph">
<p><a id="binding_relation_of_types"></a><strong>Definition:</strong> <a href="#binding_relation_of_types">Binding Relation of Types</a></p>
</div>
<div class="paragraph">
<p>We define a pseudo relation</p>
</div>
<div class="openblock">
<div class="content">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>b</mi><mi>i</mi><mi>n</mi><mi>d</mi><mi>:</mi><mi>D</mi><mi>e</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>e</mi><mi>d</mi><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>×</mo><mi>C</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>|</mo><mi>I</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>f</mi><mi>a</mi><mi>c</mi><mi>e</mi><mo>|</mo><mi>E</mi><mi>n</mi><mi>u</mi><mi>m</mi></math>
</div>
</div>
<div class="paragraph">
<p>which binds a type reference, i.e. a simple name, to the type declaration.</p>
</div>
</div>
</div>
</div>
<div class="sect3">
<h4 id="_merging-types"><a class="anchor" href="#_merging-types"></a><a class="link" href="#_merging-types">1.2.2. Merging Types</a></h4>
<div class="paragraph">
<p>In some cases we have to merge types, e.g., types of a union type or item types of an array.
For that purpose, we define a method <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>e</mi><mi>r</mi><mi>g</mi><mi>e</mi></math> as follows.</p>
</div>
<div class="openblock definition">
<div class="content">
<div class="paragraph">
<p><a id="merge_function"></a><strong>Definition:</strong> <a href="#merge_function">Merge Function</a></p>
</div>
<div class="paragraph">
<p>We define a pseudo function</p>
</div>
<div class="openblock">
<div class="content">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>m</mi><mi>e</mi><mi>r</mi><mi>g</mi><mi>e</mi><mi>:</mi><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>×</mo><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>×</mo><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi><mo>⇒</mo><mi mathvariant="script">P</mi><mfenced close=")" open="("><mrow><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi></mrow></mfenced></math>
</div>
</div>
<div class="paragraph">
<p>The idea of this function is to remove duplicates.
For example; if a union type contains two type expressions <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><msub><mi>e</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><msub><mi>e</mi><mi>k</mi></msub></math>, and if <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi><mfenced close=")" open="("><mrow><mi>t</mi><msub><mi>e</mi><mn>1</mn></msub></mrow></mfenced><mo>=</mo><mi>τ</mi><mfenced close=")" open="("><mrow><mi>t</mi><msub><mi>e</mi><mn>2</mn></msub></mrow></mfenced></math>, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>e</mi><mi>r</mi><mi>g</mi><mi>e</mi><mfenced close=")" open="("><mrow><mi>τ</mi><mfenced close=")" open="("><mrow><mi>t</mi><msub><mi>e</mi><mn>1</mn></msub></mrow></mfenced></mrow><mrow><mi>τ</mi><mfenced close=")" open="("><mrow><mi>t</mi><msub><mi>e</mi><mn>2</mn></msub></mrow></mfenced></mrow></mfenced></math> contains only one element.
The order of the elements is lost, however.</p>
</div>
</div>
</div>
<div class="sect4">
<h5 id="_logic-formulas"><a class="anchor" href="#_logic-formulas"></a><a class="link" href="#_logic-formulas">1.2.2.1. Logic Formulas</a></h5>
<div class="paragraph">
<p>In general, we use a pragmatic mixture of pseudo code, predicate logic, and OCL.
Within constraints (also within the inference rules), the properties defined in the grammar are used.</p>
</div>
<div class="paragraph">
<p>In some rules, it is necessary to type the rule variables.
Instead of explicitly checking the metatype (via <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mfenced close=")" open="("><mi>X</mi></mfenced><mo>=</mo><mi>:</mi><mrow><mi>M</mi><mi>e</mi><mi>t</mi><mi>a</mi><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi></mrow></math>), we precede the variable with the type, that is: <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>M</mi><mi>e</mi><mi>t</mi><mi>a</mi><mi>T</mi><mi>y</mi><mi>p</mi><mi>e</mi></mrow><mi>X</mi></math>.</p>
</div>
<div class="paragraph">
<p>Instead of "type casting" elements, often properties are simply accessed.
If an element does not define that element, it is either assumed to be false or null by default.</p>
</div>
<div class="paragraph">
<p>If a property <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> is optional and not set, we write <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>n</mi><mi>u</mi><mi>l</mi><mi>l</mi></math> to test its absence.
Note that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>n</mi><mi>u</mi><mi>l</mi><mi>l</mi></math> is different from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>N</mi><mi>u</mi><mi>l</mi><mi>l</mi></math>, as the latter refers to the null type.
Non-terminals may implicitly be subclasses.
In that case, the concrete non-terminal, or type, of a property may be subject for a test in a constraint.</p>
</div>
</div>
</div>
<div class="sect3">
<h4 id="_symbols-and-font-convention"><a class="anchor" href="#_symbols-and-font-convention"></a><a class="link" href="#_symbols-and-font-convention">1.2.3. Symbols and Font Convention</a></h4>
<div class="paragraph">
<p>Variables and their properties are printed in italic when used in formulas (such as rules).
A dot-notation is used for member access, e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>.</mo><mi>n</mi><mi>a</mi><mi>m</mi><mi>e</mi></math>.
Also defined functions are printed in italic, e.g., <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi>c</mi><mfenced close=")" open="("><mi>r</mi><mi>D</mi></mfenced></math>.
Properties which define sets are usually ordered and we assume 0-indexed access to elements, the index subscripted, e.g., <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>.</mo><mi>m</mi><mi>e</mi><mi>t</mi><mi>h</mi><mi>o</mi><mi>d</mi><msub><mi>s</mi><mi>i</mi></msub></math>.</p>
</div>
<div class="paragraph">
<p>We use the following symbols and font conventions:</p>
</div>
<div class="dlist">
<dl>
<dt class="hdlist1"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∧</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∨</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⊕</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>¬</mo></math></dt>
<dd>
<p>Logical and, or, exclusive or (xor), and not.</p>
</dd>
<dt class="hdlist1"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathvariant="bold"><mtext>if</mtext></mstyle><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathvariant="bold"><mtext>then</mtext></mstyle><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathvariant="bold"><mtext>else</mtext></mstyle><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/></math> </dt>
<dd>
<p>Logical implication, if and only if, and if-then-else.</p>
</dd>
<dt class="hdlist1"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathvariant="monospace"><mtext>true</mtext></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathvariant="monospace"><mtext>false</mtext></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle mathvariant="monospace"><mtext>null</mtext></mstyle></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>∅</mi></math></dt>
<dd>
<p>Boolean true, boolean false, null (i.e., not specified, e.g.,
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>.</mo><mi>s</mi><mi>u</mi><mi>p</mi><mo>=</mo></math> means that there are is no <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mi>u</mi><mi>p</mi></math>
(super class) specified), empty set.</p>
</dd>
<dt class="hdlist1"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∈</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∉</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∪</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∩</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>|</mo><mi>x</mi><mo>|</mo></math></dt>
<dd>
<p>Element of, not an element of, union set, intersection set,
cardinality of set x.</p>
</dd>
<dt class="hdlist1"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="script">P</mi><mfenced close=")" open="("><mi>X</mi></mfenced></math></dt>
<dd>
<p>Power set of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>, i.e.
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="script">P</mi><mfenced close=")" open="("><mi>X</mi></mfenced><mo>=</mo><mfenced close="}" open="{"><mrow><mi>U</mi><mi>:</mi><mi>U</mi><mo>⊆</mo><mi>X</mi></mrow></mfenced></math>.</p>
</dd>
<dt class="hdlist1"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∃</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∄</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∀</mo></math></dt>
<dd>
<p>Exists, not exists, for all; we write <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∃</mo><mi>x</mi><mo>,</mo><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>,</mo><mi>z</mi><mi>:</mi><mi>P</mi><mfenced close=")" open="("><mi>x</mi><mrow><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/></mrow><mi>z</mi></mfenced></math> and say</p>
<div class="quoteblock">
<blockquote>
"there exists <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>,</mo><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>,</mo><mi>z</mi></math> such that predicate <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> is true".
</blockquote>
</div>
<div class="paragraph">
<p>Note that <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∄</mo><mi>x</mi><mi>:</mi><mi>P</mi><mfenced close=")" open="("><mi>x</mi></mfenced><mo>⇔</mo><mo>∀</mo><mi>x</mi><mi>:</mi><mo>¬</mo><mi>P</mi><mfenced close=")" open="("><mi>x</mi></mfenced></math>.</p>
</div>
</dd>
<dt class="hdlist1"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mfenced close=")" open="("><mrow><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/></mrow></mfenced></math></dt>
<dd>
<p>(mu) read "<strong>metatype of</strong>"; metatype of a variable or property, e.g.,</p>
<div class="openblock">
<div class="content">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mstyle mathvariant="bold"><mtext>if</mtext></mstyle><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mi>μ</mi><mfenced close=")" open="("><mi>x</mi></mfenced><mo>=</mo><mi>:</mi><mrow><mi>C</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi></mrow><mstyle mathvariant="bold"><mtext>then</mtext></mstyle><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mstyle mathvariant="bold"><mtext>else</mtext></mstyle><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/></math>
</div>
</div>
</dd>
<dt class="hdlist1"><math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mi>x</mi><mo>¯</mo></mover></math></dt>
<dd>
<p>Sequence of elements <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo>,</mo><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>,</mo><msub><mi>x</mi><mi>n</mi></msub></math>. E.g., if we want to
define a constraint that the owner of a members of a class
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> is the class, we simply write</p>
<div class="openblock">
<div class="content">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>C</mi><mo>.</mo><mover accent="true"><mrow><mi>m</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>s</mi></mrow><mo>¯</mo></mover><mo>.</mo><mi>o</mi><mi>w</mi><mi>n</mi><mi>e</mi><mi>r</mi><mo>=</mo><mi>C</mi></math>
</div>
</div>
<div class="paragraph">
<p>instead of</p>
</div>
<div class="openblock">
<div class="content">
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>∀</mo><mi>m</mi><mo>∈</mo><mi>C</mi><mo>.</mo><mi>m</mi><mi>e</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mi>s</mi><mi>:</mi><mi>m</mi><mo>.</mo><mi>o</mi><mi>w</mi><mi>n</mi><mi>e</mi><mi>r</mi><mo>=</mo><mi>C</mi></math>
</div>
</div>
<div class="paragraph">
<p>or even more complicated with index variables.</p>
</div>
</dd>
</dl>
</div>
<div class="paragraph">
<p>Sequences are 1-based, e.g., a sequence <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math> with length <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>|</mo><mi>s</mi><mo>|</mo><mo>=</mo><mi>n</mi></math>, has elements <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>1</mn></msub><mo>,</mo><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>.</mo><mspace width="1.0mm"/><mo>,</mo><msub><mi>s</mi><mi>n</mi></msub></math>.</p>
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